LMFDB - Embedded newform 1512.1.ce.a.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,1,Mod(235,1512)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4, 4]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1512.235");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1512.ce (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.754586299101$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 504)
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.254016.3

Embedding invariants

Embedding label			235.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1512.235
Dual form			1512.1.ce.a.1171.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(0.866025 - 0.500000i) q^{13} -1.00000 q^{14} +1.00000 q^{16} +(-0.500000 + 0.866025i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-0.866025 + 0.500000i) q^{22} +(0.866025 + 0.500000i) q^{23} +(-0.500000 - 0.866025i) q^{26} +1.00000i q^{28} +(0.866025 + 0.500000i) q^{29} -1.00000i q^{32} +(0.866025 + 0.500000i) q^{34} +(0.500000 - 0.866025i) q^{35} +(0.866025 - 0.500000i) q^{37} +(-0.866025 + 0.500000i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(-0.500000 - 0.866025i) q^{41} +(0.500000 - 0.866025i) q^{43} +(0.500000 + 0.866025i) q^{44} +(0.500000 - 0.866025i) q^{46} -1.00000 q^{49} +(-0.866025 + 0.500000i) q^{52} +(-0.866025 - 0.500000i) q^{53} -1.00000i q^{55} +1.00000 q^{56} +(0.500000 - 0.866025i) q^{58} -1.00000 q^{64} +1.00000 q^{65} +(0.500000 - 0.866025i) q^{68} +(-0.866025 - 0.500000i) q^{70} +(-0.500000 + 0.866025i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(0.500000 + 0.866025i) q^{76} +(-0.866025 + 0.500000i) q^{77} +2.00000i q^{79} +(0.866025 + 0.500000i) q^{80} +(-0.866025 + 0.500000i) q^{82} +(-0.500000 + 0.866025i) q^{83} +(-0.866025 + 0.500000i) q^{85} +(-0.866025 - 0.500000i) q^{86} +(0.866025 - 0.500000i) q^{88} +(0.500000 + 0.866025i) q^{89} +(-0.500000 - 0.866025i) q^{91} +(-0.866025 - 0.500000i) q^{92} -1.00000i q^{95} +(-0.500000 + 0.866025i) q^{97} +1.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4}+O(q^{10}) $ 4 * q - 4 * q^4	$ 4 q - 4 q^{4} + 2 q^{10} - 2 q^{11} - 4 q^{14} + 4 q^{16} - 2 q^{17} - 2 q^{19} - 2 q^{26} + 2 q^{35} - 2 q^{40} - 2 q^{41} + 2 q^{43} + 2 q^{44} + 2 q^{46} - 4 q^{49} + 4 q^{56} + 2 q^{58} - 4 q^{64} + 4 q^{65} + 2 q^{68} - 2 q^{73} - 2 q^{74} + 2 q^{76} - 2 q^{83} + 2 q^{89} - 2 q^{91} - 2 q^{97}+O(q^{100}) $ 4 * q - 4 * q^4 + 2 * q^10 - 2 * q^11 - 4 * q^14 + 4 * q^16 - 2 * q^17 - 2 * q^19 - 2 * q^26 + 2 * q^35 - 2 * q^40 - 2 * q^41 + 2 * q^43 + 2 * q^44 + 2 * q^46 - 4 * q^49 + 4 * q^56 + 2 * q^58 - 4 * q^64 + 4 * q^65 + 2 * q^68 - 2 * q^73 - 2 * q^74 + 2 * q^76 - 2 * q^83 + 2 * q^89 - 2 * q^91 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.00000i		−	1.00000i
$2$		−	1.00000i		−	1.00000i
$3$		0			0
$3$		0			0
$4$	−1.00000			−1.00000
$5$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$5$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$6$		0			0
$7$		−	1.00000i		−	1.00000i
$7$		−	1.00000i		−	1.00000i
$8$			1.00000i			1.00000i
$9$		0			0
$10$	0.500000	−	0.866025i	0.500000	−	0.866025i
$11$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$11$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$12$		0			0
$13$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$13$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$14$	−1.00000			−1.00000
$15$		0			0
$16$	1.00000			1.00000
$17$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$17$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$18$		0			0
$19$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$19$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$20$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$21$		0			0
$22$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$23$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$23$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$24$		0			0
$25$		0			0
$26$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$27$		0			0
$28$			1.00000i			1.00000i
$29$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$29$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$		−	1.00000i		−	1.00000i
$33$		0			0
$34$	0.866025	+	0.500000i	0.866025	+	0.500000i
$35$	0.500000	−	0.866025i	0.500000	−	0.866025i
$36$		0			0
$37$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$37$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$38$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$39$		0			0
$40$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$41$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$41$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$42$		0			0
$43$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$43$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$44$	0.500000	+	0.866025i	0.500000	+	0.866025i
$45$		0			0
$46$	0.500000	−	0.866025i	0.500000	−	0.866025i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$		0			0
$49$	−1.00000			−1.00000
$50$		0			0
$51$		0			0
$52$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$53$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$53$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$54$		0			0
$55$		−	1.00000i		−	1.00000i
$56$	1.00000			1.00000
$57$		0			0
$58$	0.500000	−	0.866025i	0.500000	−	0.866025i
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$		0			0
$63$		0			0
$64$	−1.00000			−1.00000
$65$	1.00000			1.00000
$66$		0			0
$67$		0			0			−	1.00000i	$-0.5\pi$
$67$		0			0				1.00000i	$0.5\pi$
$68$	0.500000	−	0.866025i	0.500000	−	0.866025i
$69$		0			0
$70$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$73$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$74$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$75$		0			0
$76$	0.500000	+	0.866025i	0.500000	+	0.866025i
$77$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$78$		0			0
$79$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$79$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$80$	0.866025	+	0.500000i	0.866025	+	0.500000i
$81$		0			0
$82$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$83$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$83$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$84$		0			0
$85$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$86$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$87$		0			0
$88$	0.866025	−	0.500000i	0.866025	−	0.500000i
$89$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$89$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$90$		0			0
$91$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$92$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$93$		0			0
$94$		0			0
$95$		−	1.00000i		−	1.00000i
$96$		0			0
$97$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$97$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$98$			1.00000i			1.00000i
$99$		0			0
$100$		0			0
$101$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$101$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$103$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$104$	0.500000	+	0.866025i	0.500000	+	0.866025i
$105$		0			0
$106$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$107$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$107$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$108$		0			0
$109$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$109$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$110$	−1.00000			−1.00000
$111$		0			0
$112$		−	1.00000i		−	1.00000i
$113$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$113$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$114$		0			0
$115$	0.500000	+	0.866025i	0.500000	+	0.866025i
$116$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$117$		0			0
$118$		0			0
$119$	0.866025	+	0.500000i	0.866025	+	0.500000i
$120$		0			0
$121$		0			0
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	1.00000i		−	1.00000i
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$			1.00000i			1.00000i
$129$		0			0
$130$		−	1.00000i		−	1.00000i
$131$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$131$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$132$		0			0
$133$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$134$		0			0
$135$		0			0
$136$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$137$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$137$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$139$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$140$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$141$		0			0
$142$		0			0
$143$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$144$		0			0
$145$	0.500000	+	0.866025i	0.500000	+	0.866025i
$146$	0.866025	+	0.500000i	0.866025	+	0.500000i
$147$		0			0
$148$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$149$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$149$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$150$		0			0
$151$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$151$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$152$	0.866025	−	0.500000i	0.866025	−	0.500000i
$153$		0			0
$154$	0.500000	+	0.866025i	0.500000	+	0.866025i
$155$		0			0
$156$		0			0
$157$		0			0		1.00000			$0$
$157$		0			0		−1.00000			$\pi$
$158$	2.00000			2.00000
$159$		0			0
$160$	0.500000	−	0.866025i	0.500000	−	0.866025i
$161$	0.500000	−	0.866025i	0.500000	−	0.866025i
$162$		0			0
$163$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$163$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$164$	0.500000	+	0.866025i	0.500000	+	0.866025i
$165$		0			0
$166$	0.866025	+	0.500000i	0.866025	+	0.500000i
$167$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$167$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$168$		0			0
$169$		0			0
$170$	0.500000	+	0.866025i	0.500000	+	0.866025i
$171$		0			0
$172$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$173$		0			0		1.00000			$0$
$173$		0			0		−1.00000			$\pi$
$174$		0			0
$175$		0			0
$176$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$177$		0			0
$178$	0.866025	−	0.500000i	0.866025	−	0.500000i
$179$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$179$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$180$		0			0
$181$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$181$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$182$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$183$		0			0
$184$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$185$	1.00000			1.00000
$186$		0			0
$187$	1.00000			1.00000
$188$		0			0
$189$		0			0
$190$	−1.00000			−1.00000
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$		0			0
$193$		0			0			−	1.00000i	$-0.5\pi$
$193$		0			0				1.00000i	$0.5\pi$
$194$	0.866025	+	0.500000i	0.866025	+	0.500000i
$195$		0			0
$196$	1.00000			1.00000
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$199$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$200$		0			0
$201$		0			0
$202$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$203$	0.500000	−	0.866025i	0.500000	−	0.866025i
$204$		0			0
$205$		−	1.00000i		−	1.00000i
$206$	0.500000	−	0.866025i	0.500000	−	0.866025i
$207$		0			0
$208$	0.866025	−	0.500000i	0.866025	−	0.500000i
$209$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$210$		0			0
$211$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$211$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$212$	0.866025	+	0.500000i	0.866025	+	0.500000i
$213$		0			0
$214$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$215$	0.866025	−	0.500000i	0.866025	−	0.500000i
$216$		0			0
$217$		0			0
$218$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$219$		0			0
$220$			1.00000i			1.00000i
$221$			1.00000i			1.00000i
$222$		0			0
$223$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$223$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$224$	−1.00000			−1.00000
$225$		0			0
$226$	0.866025	−	0.500000i	0.866025	−	0.500000i
$227$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$227$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$228$		0			0
$229$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$229$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$230$	0.866025	−	0.500000i	0.866025	−	0.500000i
$231$		0			0
$232$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$233$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$233$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	0.500000	−	0.866025i	0.500000	−	0.866025i
$239$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$239$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$241$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$246$		0			0
$247$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$248$		0			0
$249$		0			0
$250$	−1.00000			−1.00000
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		−	1.00000i		−	1.00000i
$254$		0			0
$255$		0			0
$256$	1.00000			1.00000
$257$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$257$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$258$		0			0
$259$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$260$	−1.00000			−1.00000
$261$		0			0
$262$	0.866025	+	0.500000i	0.866025	+	0.500000i
$263$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$263$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$266$	0.500000	+	0.866025i	0.500000	+	0.866025i
$267$		0			0
$268$		0			0
$269$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$269$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$270$		0			0
$271$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$271$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$272$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$273$		0			0
$274$	0.866025	−	0.500000i	0.866025	−	0.500000i
$275$		0			0
$276$		0			0
$277$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$277$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$278$	0.866025	−	0.500000i	0.866025	−	0.500000i
$279$		0			0
$280$	0.866025	+	0.500000i	0.866025	+	0.500000i
$281$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$281$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$282$		0			0
$283$		0			0			−	1.00000i	$-0.5\pi$
$283$		0			0				1.00000i	$0.5\pi$
$284$		0			0
$285$		0			0
$286$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$287$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$288$		0			0
$289$		0			0
$290$	0.866025	−	0.500000i	0.866025	−	0.500000i
$291$		0			0
$292$	0.500000	−	0.866025i	0.500000	−	0.866025i
$293$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$293$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$294$		0			0
$295$		0			0
$296$	0.500000	+	0.866025i	0.500000	+	0.866025i
$297$		0			0
$298$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$299$	1.00000			1.00000
$300$		0			0
$301$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$302$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$303$		0			0
$304$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$305$		0			0
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$	0.866025	−	0.500000i	0.866025	−	0.500000i
$309$		0			0
$310$		0			0
$311$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$311$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$312$		0			0
$313$		0			0			−	1.00000i	$-0.5\pi$
$313$		0			0				1.00000i	$0.5\pi$
$314$		0			0
$315$		0			0
$316$		−	2.00000i		−	2.00000i
$317$		0			0		1.00000			$0$
$317$		0			0		−1.00000			$\pi$
$318$		0			0
$319$		−	1.00000i		−	1.00000i
$320$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$321$		0			0
$322$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$323$	1.00000			1.00000
$324$		0			0
$325$		0			0
$326$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$327$		0			0
$328$	0.866025	−	0.500000i	0.866025	−	0.500000i
$329$		0			0
$330$		0			0
$331$		0			0			−	1.00000i	$-0.5\pi$
$331$		0			0				1.00000i	$0.5\pi$
$332$	0.500000	−	0.866025i	0.500000	−	0.866025i
$333$		0			0
$334$	0.500000	+	0.866025i	0.500000	+	0.866025i
$335$		0			0
$336$		0			0
$337$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$337$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$338$		0			0
$339$		0			0
$340$	0.866025	−	0.500000i	0.866025	−	0.500000i
$341$		0			0
$342$		0			0
$343$			1.00000i			1.00000i
$344$	0.866025	+	0.500000i	0.866025	+	0.500000i
$345$		0			0
$346$		0			0
$347$		0			0			−	1.00000i	$-0.5\pi$
$347$		0			0				1.00000i	$0.5\pi$
$348$		0			0
$349$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$349$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$350$		0			0
$351$		0			0
$352$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$353$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$353$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$354$		0			0
$355$		0			0
$356$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$357$		0			0
$358$	0.866025	+	0.500000i	0.866025	+	0.500000i
$359$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$359$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$360$		0			0
$361$		0			0
$362$	2.00000			2.00000
$363$		0			0
$364$	0.500000	+	0.866025i	0.500000	+	0.866025i
$365$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$366$		0			0
$367$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$367$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$368$	0.866025	+	0.500000i	0.866025	+	0.500000i
$369$		0			0
$370$		−	1.00000i		−	1.00000i
$371$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$372$		0			0
$373$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$373$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$374$		−	1.00000i		−	1.00000i
$375$		0			0
$376$		0			0
$377$	1.00000			1.00000
$378$		0			0
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$			1.00000i			1.00000i
$381$		0			0
$382$		0			0
$383$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$383$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$384$		0			0
$385$	−1.00000			−1.00000
$386$		0			0
$387$		0			0
$388$	0.500000	−	0.866025i	0.500000	−	0.866025i
$389$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$389$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$390$		0			0
$391$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$392$		−	1.00000i		−	1.00000i
$393$		0			0
$394$		0			0
$395$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$396$		0			0
$397$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$397$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$398$	0.500000	−	0.866025i	0.500000	−	0.866025i
$399$		0			0
$400$		0			0
$401$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$401$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$402$		0			0
$403$		0			0
$404$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$405$		0			0
$406$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$407$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$408$		0			0
$409$		0			0			−	1.00000i	$-0.5\pi$
$409$		0			0				1.00000i	$0.5\pi$
$410$	−1.00000			−1.00000
$411$		0			0
$412$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$413$		0			0
$414$		0			0
$415$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$416$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$417$		0			0
$418$	0.866025	+	0.500000i	0.866025	+	0.500000i
$419$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$419$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$420$		0			0
$421$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$421$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$422$	0.866025	−	0.500000i	0.866025	−	0.500000i
$423$		0			0
$424$	0.500000	−	0.866025i	0.500000	−	0.866025i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.500000	+	0.866025i	0.500000	+	0.866025i
$429$		0			0
$430$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$431$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$431$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$432$		0			0
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$		0			0
$435$		0			0
$436$	0.866025	+	0.500000i	0.866025	+	0.500000i
$437$		−	1.00000i		−	1.00000i
$438$		0			0
$439$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$439$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$440$	1.00000			1.00000
$441$		0			0
$442$	1.00000			1.00000
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$		0			0
$445$			1.00000i			1.00000i
$446$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$447$		0			0
$448$			1.00000i			1.00000i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$		0			0
$451$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$452$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$453$		0			0
$454$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$455$		−	1.00000i		−	1.00000i
$456$		0			0
$457$	−2.00000			−2.00000			−1.00000			$\pi$
$457$	−2.00000			−2.00000			−1.00000			$\pi$
$458$	0.500000	−	0.866025i	0.500000	−	0.866025i
$459$		0			0
$460$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$461$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$461$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$462$		0			0
$463$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$463$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$464$	0.866025	+	0.500000i	0.866025	+	0.500000i
$465$		0			0
$466$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$467$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$467$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.00000			−1.00000
$474$		0			0
$475$		0			0
$476$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$477$		0			0
$478$	0.500000	+	0.866025i	0.500000	+	0.866025i
$479$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$479$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$480$		0			0
$481$	0.500000	−	0.866025i	0.500000	−	0.866025i
$482$	0.866025	−	0.500000i	0.866025	−	0.500000i
$483$		0			0
$484$		0			0
$485$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$486$		0			0
$487$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$487$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$488$		0			0
$489$		0			0
$490$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$491$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$491$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$492$		0			0
$493$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$494$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$499$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$500$			1.00000i			1.00000i
$501$		0			0
$502$		0			0
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$	1.00000			1.00000
$506$	−1.00000			−1.00000
$507$		0			0
$508$		0			0
$509$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$509$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$510$		0			0
$511$	0.866025	+	0.500000i	0.866025	+	0.500000i
$512$		−	1.00000i		−	1.00000i
$513$		0			0
$514$	0.866025	+	0.500000i	0.866025	+	0.500000i
$515$	0.500000	+	0.866025i	0.500000	+	0.866025i
$516$		0			0
$517$		0			0
$518$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$519$		0			0
$520$			1.00000i			1.00000i
$521$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$521$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$522$		0			0
$523$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$523$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$524$	0.500000	−	0.866025i	0.500000	−	0.866025i
$525$		0			0
$526$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$527$		0			0
$528$		0			0
$529$		0			0
$530$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$531$		0			0
$532$	0.866025	−	0.500000i	0.866025	−	0.500000i
$533$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$534$		0			0
$535$		−	1.00000i		−	1.00000i
$536$		0			0
$537$		0			0
$538$	0.500000	−	0.866025i	0.500000	−	0.866025i
$539$	0.500000	+	0.866025i	0.500000	+	0.866025i
$540$		0			0
$541$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$541$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$542$	0.500000	+	0.866025i	0.500000	+	0.866025i
$543$		0			0
$544$	0.866025	+	0.500000i	0.866025	+	0.500000i
$545$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$546$		0			0
$547$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$547$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$548$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$549$		0			0
$550$		0			0
$551$		−	1.00000i		−	1.00000i
$552$		0			0
$553$	2.00000			2.00000
$554$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$555$		0			0
$556$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$557$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$557$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$558$		0			0
$559$		−	1.00000i		−	1.00000i
$560$	0.500000	−	0.866025i	0.500000	−	0.866025i
$561$		0			0
$562$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$563$		0			0			−	1.00000i	$-0.5\pi$
$563$		0			0				1.00000i	$0.5\pi$
$564$		0			0
$565$			1.00000i			1.00000i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.00000			−2.00000			−1.00000			$\pi$
$569$	−2.00000			−2.00000			−1.00000			$\pi$
$570$		0			0
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$	0.866025	+	0.500000i	0.866025	+	0.500000i
$573$		0			0
$574$	0.500000	+	0.866025i	0.500000	+	0.866025i
$575$		0			0
$576$		0			0
$577$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$577$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$578$		0			0
$579$		0			0
$580$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$581$	0.866025	+	0.500000i	0.866025	+	0.500000i
$582$		0			0
$583$			1.00000i			1.00000i
$584$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$585$		0			0
$586$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$587$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$587$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.866025	−	0.500000i	0.866025	−	0.500000i
$593$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$593$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$594$		0			0
$595$	0.500000	+	0.866025i	0.500000	+	0.866025i
$596$	0.866025	+	0.500000i	0.866025	+	0.500000i
$597$		0			0
$598$		−	1.00000i		−	1.00000i
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$		0			0
$601$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$601$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$602$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$603$		0			0
$604$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$605$		0			0
$606$		0			0
$607$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$607$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$608$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$613$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$614$		0			0
$615$		0			0
$616$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$617$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$617$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$618$		0			0
$619$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$619$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$620$		0			0
$621$		0			0
$622$	2.00000			2.00000
$623$	0.866025	−	0.500000i	0.866025	−	0.500000i
$624$		0			0
$625$	0.500000	−	0.866025i	0.500000	−	0.866025i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			1.00000i			1.00000i
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$	−2.00000			−2.00000
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$638$	−1.00000			−1.00000
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$641$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$641$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$642$		0			0
$643$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$643$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$644$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$645$		0			0
$646$		−	1.00000i		−	1.00000i
$647$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$647$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.500000	+	0.866025i	0.500000	+	0.866025i
$653$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$653$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$654$		0			0
$655$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$656$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$657$		0			0
$658$		0			0
$659$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$659$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$660$		0			0
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$		0			0
$663$		0			0
$664$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$665$	−1.00000			−1.00000
$666$		0			0
$667$	0.500000	+	0.866025i	0.500000	+	0.866025i
$668$	0.866025	−	0.500000i	0.866025	−	0.500000i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$673$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$674$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$675$		0			0
$676$		0			0
$677$		0			0		1.00000			$0$
$677$		0			0		−1.00000			$\pi$
$678$		0			0
$679$	0.866025	+	0.500000i	0.866025	+	0.500000i
$680$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$681$		0			0
$682$		0			0
$683$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$683$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$684$		0			0
$685$			1.00000i			1.00000i
$686$	1.00000			1.00000
$687$		0			0
$688$	0.500000	−	0.866025i	0.500000	−	0.866025i
$689$	−1.00000			−1.00000
$690$		0			0
$691$		0			0			−	1.00000i	$-0.5\pi$
$691$		0			0				1.00000i	$0.5\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			1.00000i			1.00000i
$696$		0			0
$697$	1.00000			1.00000
$698$	0.500000	−	0.866025i	0.500000	−	0.866025i
$699$		0			0
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$704$	0.500000	+	0.866025i	0.500000	+	0.866025i
$705$		0			0
$706$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$707$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$708$		0			0
$709$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$709$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$710$		0			0
$711$		0			0
$712$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$713$		0			0
$714$		0			0
$715$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$716$	0.500000	−	0.866025i	0.500000	−	0.866025i
$717$		0			0
$718$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$719$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$719$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$720$		0			0
$721$	0.500000	−	0.866025i	0.500000	−	0.866025i
$722$		0			0
$723$		0			0
$724$		−	2.00000i		−	2.00000i
$725$		0			0
$726$		0			0
$727$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$727$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$728$	0.866025	−	0.500000i	0.866025	−	0.500000i
$729$		0			0
$730$	0.500000	+	0.866025i	0.500000	+	0.866025i
$731$	0.500000	+	0.866025i	0.500000	+	0.866025i
$732$		0			0
$733$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$733$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$734$	0.500000	+	0.866025i	0.500000	+	0.866025i
$735$		0			0
$736$	0.500000	−	0.866025i	0.500000	−	0.866025i
$737$		0			0
$738$		0			0
$739$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$739$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$740$	−1.00000			−1.00000
$741$		0			0
$742$	0.866025	+	0.500000i	0.866025	+	0.500000i
$743$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$743$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$744$		0			0
$745$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$746$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$747$		0			0
$748$	−1.00000			−1.00000
$749$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$750$		0			0
$751$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$751$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$752$		0			0
$753$		0			0
$754$		−	1.00000i		−	1.00000i
$755$	1.00000			1.00000
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$	1.00000			1.00000
$761$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$761$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$762$		0			0
$763$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$764$		0			0
$765$		0			0
$766$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$767$		0			0
$768$		0			0
$769$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$769$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$770$			1.00000i			1.00000i
$771$		0			0
$772$		0			0
$773$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$773$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$774$		0			0
$775$		0			0
$776$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$777$		0			0
$778$	0.500000	+	0.866025i	0.500000	+	0.866025i
$779$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$780$		0			0
$781$		0			0
$782$	0.500000	+	0.866025i	0.500000	+	0.866025i
$783$		0			0
$784$	−1.00000			−1.00000
$785$		0			0
$786$		0			0
$787$		0			0			−	1.00000i	$-0.5\pi$
$787$		0			0				1.00000i	$0.5\pi$
$788$		0			0
$789$		0			0
$790$	1.73205	+	1.00000i	1.73205	+	1.00000i
$791$	0.866025	−	0.500000i	0.866025	−	0.500000i
$792$		0			0
$793$		0			0
$794$	0.500000	+	0.866025i	0.500000	+	0.866025i
$795$		0			0
$796$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$797$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$797$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$803$	1.00000			1.00000
$804$		0			0
$805$	0.866025	−	0.500000i	0.866025	−	0.500000i
$806$		0			0
$807$		0			0
$808$	0.500000	+	0.866025i	0.500000	+	0.866025i
$809$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$809$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$810$		0			0
$811$	−2.00000			−2.00000			−1.00000			$\pi$
$811$	−2.00000			−2.00000			−1.00000			$\pi$
$812$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$813$		0			0
$814$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$815$		−	1.00000i		−	1.00000i
$816$		0			0
$817$	−1.00000			−1.00000
$818$		0			0
$819$		0			0
$820$			1.00000i			1.00000i
$821$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$821$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$822$		0			0
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$825$		0			0
$826$		0			0
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$		0			0
$829$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$829$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$830$	0.500000	+	0.866025i	0.500000	+	0.866025i
$831$		0			0
$832$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$833$	0.500000	−	0.866025i	0.500000	−	0.866025i
$834$		0			0
$835$	−1.00000			−1.00000
$836$	0.500000	−	0.866025i	0.500000	−	0.866025i
$837$		0			0
$838$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$839$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$839$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$840$		0			0
$841$		0			0
$842$	0.500000	−	0.866025i	0.500000	−	0.866025i
$843$		0			0
$844$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$845$		0			0
$846$		0			0
$847$		0			0
$848$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$849$		0			0
$850$		0			0
$851$	1.00000			1.00000
$852$		0			0
$853$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$853$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$854$		0			0
$855$		0			0
$856$	0.866025	−	0.500000i	0.866025	−	0.500000i
$857$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$857$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$858$		0			0
$859$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$859$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$860$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$861$		0			0
$862$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$863$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$863$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.73205	−	1.00000i	1.73205	−	1.00000i
$870$		0			0
$871$		0			0
$872$	0.500000	−	0.866025i	0.500000	−	0.866025i
$873$		0			0
$874$	−1.00000			−1.00000
$875$	−1.00000			−1.00000
$876$		0			0
$877$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$877$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$878$	−2.00000			−2.00000
$879$		0			0
$880$		−	1.00000i		−	1.00000i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$		−	1.00000i		−	1.00000i
$885$		0			0
$886$		0			0
$887$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$887$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$888$		0			0
$889$		0			0
$890$	1.00000			1.00000
$891$		0			0
$892$	0.866025	+	0.500000i	0.866025	+	0.500000i
$893$		0			0
$894$		0			0
$895$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$896$	1.00000			1.00000
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	0.866025	−	0.500000i	0.866025	−	0.500000i
$902$	0.866025	+	0.500000i	0.866025	+	0.500000i
$903$		0			0
$904$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$905$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$906$		0			0
$907$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$907$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$908$	0.500000	+	0.866025i	0.500000	+	0.866025i
$909$		0			0
$910$	−1.00000			−1.00000
$911$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$911$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$912$		0			0
$913$	1.00000			1.00000
$914$			2.00000i			2.00000i
$915$		0			0
$916$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$917$	0.866025	+	0.500000i	0.866025	+	0.500000i
$918$		0			0
$919$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$919$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$920$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$921$		0			0
$922$	0.500000	−	0.866025i	0.500000	−	0.866025i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	0.500000	+	0.866025i	0.500000	+	0.866025i
$927$		0			0
$928$	0.500000	−	0.866025i	0.500000	−	0.866025i
$929$		0			0			−	1.00000i	$-0.5\pi$
$929$		0			0				1.00000i	$0.5\pi$
$930$		0			0
$931$	0.500000	+	0.866025i	0.500000	+	0.866025i
$932$	0.500000	+	0.866025i	0.500000	+	0.866025i
$933$		0			0
$934$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$935$	0.866025	+	0.500000i	0.866025	+	0.500000i
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$		0			0
$943$		−	1.00000i		−	1.00000i
$944$		0			0
$945$		0			0
$946$			1.00000i			1.00000i
$947$	2.00000			2.00000			1.00000			$0$
$947$	2.00000			2.00000			1.00000			$0$
$948$		0			0
$949$			1.00000i			1.00000i
$950$		0			0
$951$		0			0
$952$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$		0			0
$955$		0			0
$956$	0.866025	−	0.500000i	0.866025	−	0.500000i
$957$		0			0
$958$	0.500000	+	0.866025i	0.500000	+	0.866025i
$959$	0.866025	−	0.500000i	0.866025	−	0.500000i
$960$		0			0
$961$	1.00000			1.00000
$962$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$963$		0			0
$964$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$965$		0			0
$966$		0			0
$967$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$967$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$968$		0			0
$969$		0			0
$970$	0.500000	+	0.866025i	0.500000	+	0.866025i
$971$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$971$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$972$		0			0
$973$	0.866025	−	0.500000i	0.866025	−	0.500000i
$974$	0.500000	−	0.866025i	0.500000	−	0.866025i
$975$		0			0
$976$		0			0
$977$		0			0			−	1.00000i	$-0.5\pi$
$977$		0			0				1.00000i	$0.5\pi$
$978$		0			0
$979$	0.500000	−	0.866025i	0.500000	−	0.866025i
$980$	0.866025	+	0.500000i	0.866025	+	0.500000i
$981$		0			0
$982$	0.866025	−	0.500000i	0.866025	−	0.500000i
$983$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$983$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$984$		0			0
$985$		0			0
$986$	0.500000	+	0.866025i	0.500000	+	0.866025i
$987$		0			0
$988$	0.866025	+	0.500000i	0.866025	+	0.500000i
$989$	0.866025	−	0.500000i	0.866025	−	0.500000i
$990$		0			0
$991$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$991$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.500000	+	0.866025i	0.500000	+	0.866025i
$996$		0			0
$997$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$997$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$998$	0.866025	+	0.500000i	0.866025	+	0.500000i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.1.ce.a.235.1		4
3.2	odd	2		504.1.ce.a.403.2	yes	4
7.2	even	3		1512.1.ba.a.667.1		4
8.3	odd	2	inner	1512.1.ce.a.235.2		4
9.4	even	3		1512.1.ba.a.739.2		4
9.5	odd	6		504.1.ba.a.67.1	✓	4
12.11	even	2		2016.1.cm.a.655.1		4
21.2	odd	6		504.1.ba.a.331.2	yes	4
21.5	even	6		3528.1.ba.d.1843.2		4
21.11	odd	6		3528.1.cg.d.2059.1		4
21.17	even	6		3528.1.cg.c.2059.1		4
21.20	even	2		3528.1.ce.c.2419.2		4
24.5	odd	2		2016.1.cm.a.655.2		4
24.11	even	2		504.1.ce.a.403.1	yes	4
36.23	even	6		2016.1.bi.a.1327.2		4
56.51	odd	6		1512.1.ba.a.667.2		4
63.5	even	6		3528.1.ce.c.3019.2		4
63.23	odd	6		504.1.ce.a.499.2	yes	4
63.32	odd	6		3528.1.cg.d.3235.2		4
63.41	even	6		3528.1.ba.d.67.1		4
63.58	even	3	inner	1512.1.ce.a.1171.1		4
63.59	even	6		3528.1.cg.c.3235.2		4
72.5	odd	6		2016.1.bi.a.1327.1		4
72.59	even	6		504.1.ba.a.67.2	yes	4
72.67	odd	6		1512.1.ba.a.739.1		4
84.23	even	6		2016.1.bi.a.79.2		4
168.11	even	6		3528.1.cg.d.2059.2		4
168.59	odd	6		3528.1.cg.c.2059.2		4
168.83	odd	2		3528.1.ce.c.2419.1		4
168.107	even	6		504.1.ba.a.331.1	yes	4
168.131	odd	6		3528.1.ba.d.1843.1		4
168.149	odd	6		2016.1.bi.a.79.1		4
252.23	even	6		2016.1.cm.a.751.2		4
504.59	odd	6		3528.1.cg.c.3235.1		4
504.131	odd	6		3528.1.ce.c.3019.1		4
504.149	odd	6		2016.1.cm.a.751.1		4
504.275	even	6		504.1.ce.a.499.1	yes	4
504.347	even	6		3528.1.cg.d.3235.1		4
504.419	odd	6		3528.1.ba.d.67.2		4
504.499	odd	6	inner	1512.1.ce.a.1171.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.1.ba.a.67.1	✓	4	9.5	odd	6
504.1.ba.a.67.2	yes	4	72.59	even	6
504.1.ba.a.331.1	yes	4	168.107	even	6
504.1.ba.a.331.2	yes	4	21.2	odd	6
504.1.ce.a.403.1	yes	4	24.11	even	2
504.1.ce.a.403.2	yes	4	3.2	odd	2
504.1.ce.a.499.1	yes	4	504.275	even	6
504.1.ce.a.499.2	yes	4	63.23	odd	6
1512.1.ba.a.667.1		4	7.2	even	3
1512.1.ba.a.667.2		4	56.51	odd	6
1512.1.ba.a.739.1		4	72.67	odd	6
1512.1.ba.a.739.2		4	9.4	even	3
1512.1.ce.a.235.1		4	1.1	even	1	trivial
1512.1.ce.a.235.2		4	8.3	odd	2	inner
1512.1.ce.a.1171.1		4	63.58	even	3	inner
1512.1.ce.a.1171.2		4	504.499	odd	6	inner
2016.1.bi.a.79.1		4	168.149	odd	6
2016.1.bi.a.79.2		4	84.23	even	6
2016.1.bi.a.1327.1		4	72.5	odd	6
2016.1.bi.a.1327.2		4	36.23	even	6
2016.1.cm.a.655.1		4	12.11	even	2
2016.1.cm.a.655.2		4	24.5	odd	2
2016.1.cm.a.751.1		4	504.149	odd	6
2016.1.cm.a.751.2		4	252.23	even	6
3528.1.ba.d.67.1		4	63.41	even	6
3528.1.ba.d.67.2		4	504.419	odd	6
3528.1.ba.d.1843.1		4	168.131	odd	6
3528.1.ba.d.1843.2		4	21.5	even	6
3528.1.ce.c.2419.1		4	168.83	odd	2
3528.1.ce.c.2419.2		4	21.20	even	2
3528.1.ce.c.3019.1		4	504.131	odd	6
3528.1.ce.c.3019.2		4	63.5	even	6
3528.1.cg.c.2059.1		4	21.17	even	6
3528.1.cg.c.2059.2		4	168.59	odd	6
3528.1.cg.c.3235.1		4	504.59	odd	6
3528.1.cg.c.3235.2		4	63.59	even	6
3528.1.cg.d.2059.1		4	21.11	odd	6
3528.1.cg.d.2059.2		4	168.11	even	6
3528.1.cg.d.3235.1		4	504.347	even	6
3528.1.cg.d.3235.2		4	63.32	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1512.ce (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(0.866025 - 0.500000i) q^{13} -1.00000 q^{14} +1.00000 q^{16} +(-0.500000 + 0.866025i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-0.866025 + 0.500000i) q^{22} +(0.866025 + 0.500000i) q^{23} +(-0.500000 - 0.866025i) q^{26} +1.00000i q^{28} +(0.866025 + 0.500000i) q^{29} -1.00000i q^{32} +(0.866025 + 0.500000i) q^{34} +(0.500000 - 0.866025i) q^{35} +(0.866025 - 0.500000i) q^{37} +(-0.866025 + 0.500000i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(-0.500000 - 0.866025i) q^{41} +(0.500000 - 0.866025i) q^{43} +(0.500000 + 0.866025i) q^{44} +(0.500000 - 0.866025i) q^{46} -1.00000 q^{49} +(-0.866025 + 0.500000i) q^{52} +(-0.866025 - 0.500000i) q^{53} -1.00000i q^{55} +1.00000 q^{56} +(0.500000 - 0.866025i) q^{58} -1.00000 q^{64} +1.00000 q^{65} +(0.500000 - 0.866025i) q^{68} +(-0.866025 - 0.500000i) q^{70} +(-0.500000 + 0.866025i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(0.500000 + 0.866025i) q^{76} +(-0.866025 + 0.500000i) q^{77} +2.00000i q^{79} +(0.866025 + 0.500000i) q^{80} +(-0.866025 + 0.500000i) q^{82} +(-0.500000 + 0.866025i) q^{83} +(-0.866025 + 0.500000i) q^{85} +(-0.866025 - 0.500000i) q^{86} +(0.866025 - 0.500000i) q^{88} +(0.500000 + 0.866025i) q^{89} +(-0.500000 - 0.866025i) q^{91} +(-0.866025 - 0.500000i) q^{92} -1.00000i q^{95} +(-0.500000 + 0.866025i) q^{97} +1.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4}+O(q^{10}) \) 4 * q - 4 * q^4	\( 4 q - 4 q^{4} + 2 q^{10} - 2 q^{11} - 4 q^{14} + 4 q^{16} - 2 q^{17} - 2 q^{19} - 2 q^{26} + 2 q^{35} - 2 q^{40} - 2 q^{41} + 2 q^{43} + 2 q^{44} + 2 q^{46} - 4 q^{49} + 4 q^{56} + 2 q^{58} - 4 q^{64} + 4 q^{65} + 2 q^{68} - 2 q^{73} - 2 q^{74} + 2 q^{76} - 2 q^{83} + 2 q^{89} - 2 q^{91} - 2 q^{97}+O(q^{100}) \) 4 * q - 4 * q^4 + 2 * q^10 - 2 * q^11 - 4 * q^14 + 4 * q^16 - 2 * q^17 - 2 * q^19 - 2 * q^26 + 2 * q^35 - 2 * q^40 - 2 * q^41 + 2 * q^43 + 2 * q^44 + 2 * q^46 - 4 * q^49 + 4 * q^56 + 2 * q^58 - 4 * q^64 + 4 * q^65 + 2 * q^68 - 2 * q^73 - 2 * q^74 + 2 * q^76 - 2 * q^83 + 2 * q^89 - 2 * q^91 - 2 * q^97

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